That statement from the documentation is somewhat misleading; the virtual table itself does not store data in the database, but the engine that implements the virtual table might choose to use other tables to store the data.
What happens for FTS is explained in section 9.1 of the documentation:
For each FTS virtual table in a database, three to five real (non-virtual) tables are created to store the underlying data. These real tables are called "shadow tables". The real tables are named "%_content", "%_segdir", "%_segments", "%_stat", and "%_docsize", where "%" is replaced by the name of the FTS virtual table.